in Fluid Media. Bip 
To prove that the expression (3.) satisfies the equation (2.), it may be 
remarked, that we readily get, by differentiating (3.) 
Ph PH Pp awdh owe (WE, PF PY 
co dz — abe da * abe \da® + ba oe 
~ ie (satan tae) GE) + (2 ~ Gs 
Moreover, by the same means, the last of the equations (4.) gives 
pes 
Sage OD O-as 
a’ wt Bue 
Q 
af @f @f #1 Rte 
and de tay* dee Fe 
c 
which values being substituted in the second member of the preceding equa- 
tion, evidently cause it to vanish, and we thus perceive that the value (3.) 
satisfies the partial differential equation (2.) 
We will now endeavour so to determine the constant quantities \ and 
y that the fluid particles may move along the surface of the ellipsoidal body 
of which the equation is 
y 2 
2 et ERE SS, Sob I RRS (5.) 
But, by differentiation, there results 
adxw , ydy , zdz 
weiss aie Baadiee 
and as the particles must move along the surface, it is clear that the last 
equation ought to subsist, when we change the elements da, dy and da in- 
to their corresponding velocities eal 3 4? and 1¢. Hence, at this sur- 
da’ dy dz 
face, 
But the expression (3.) gives generally 
VOL. XIII. PART I. H 
